SOLUTION: a card is taken at random from a pack of cards and replaced. A second card is drawn. The probability of a diamond being drawn is one quarter. What is the probability that exactly o

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Question 352138: a card is taken at random from a pack of cards and replaced. A second card is drawn. The probability of a diamond being drawn is one quarter. What is the probability that exactly one card is a diamond?
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
Hi,
*Note: exactly one card being a diamond: the other one chosen would not be a diamond.
The probability of a diamond being drawn is 1/4 or .25
The probability of a card not being a diamond is 3/4 or .75
.
The probability of x successes in n trials is:
P = nCx* p%5Ex*q%5E%28n-x%29 where p and q are the probabilities of success and failure respectively.
.
nCx = n%21%2F%28x%21%28n-x%29%21%29
.
Of the two drawn(replacing the first), the probability of exactly one card of the two being a diamond is:
2C1 = +2%21%2F%281%21%2A0%21%29%21=+1+
.
P= 1%2A.25%5E1%2A.75%5E1 =.1875